Five-axis flank milling of impellers: Optimal geometry of a conical tool considering stiffness and geometric constraints

Abstract

Based on the Rayleigh–Ritz method, this article proposes an indicator to quantify the stiffness of a conical cutter for flank milling of impellers. Its validity is verified by the finite element analysis. A mathematical model is then developed to optimize the geometry of the conical cutter. The objective is to improve the stiffness of the cutter. Three kinds of geometric constraints are considered. First, the ball end of the cutter should be tangential to the hub surface. Second, the cutter should be interference-free with the adjacent blade. Finally, the machining error should satisfy the precision requirements. All these geometric constraints are characterized by the signed point-to-surface distance function. Based on the differential property of the distance function, a sequential linear programming method is applied to obtain the optimal geometry of the cutter along with the tool path. Simulation results confirm the effectiveness of the proposed model and algorithm.

Towards efficient 5-axis flank CNC machining of free-form surfaces via fitting envelopes of surfaces of revolution

“…In the "Initialization" columns, we show the type of initialization; whether it was line-driven (L-D) or surface-driven (S-D). The error ε ini refers to the one sided distance between the initial envelope and the reference surface, see (13). In the "Optimization", we show the number of points p sampled on the ruled surfaces in the s and t-parameter directions, respectively, and the errors after optimization.…”

“…The work of Zhu et al [30] is the closest one to our research as it also deals with flank milling and the simultaneous optimization for tool's motion and shape. This approach has been extended in [13], considering additional constraints such as conical tools and their stiffness. In both cases, the primary objective is to improve the machining process by reducing deflection and vibrations of the cutter.…”

Automatic fitting of conical envelopes to free-form surfaces for flank CNC machining

“…1. In particular, we focus on the case of conical milling tools [17,18,37,20,8,27], which are the most frequently used tools for flank milling [26]. Typically, conical milling tools are provided by a ball tip, see Fig.…”

“…and the shape of the cutter [36,20,3]. Redonnet et al [24] consider a cylindrical cutter for machining ruled surfaces and optimize its position such that it possess a tangential contact to three particular lines: one ruling of the surface and two tangent lines of the rail curves of the ruled surface.…”

“…Driven by industrial demands, efficient and high-precision manufacturing methods of free-form surfaces have been an active field for several decades [8,24,2,15,4,5,20,1]. Manufacturing of free-form objects in a serial manner is typically realized using molds where a material (e.g., heated to become flexible) is pasted between the molds to form the desired shape.…”